The book should not be used with young pupils; it is essential that the various topics should be first introduced as in Practical Geometry or Junior Geometry. Special points in this book are:1. The various topics are arranged in chapters which are more

or less self-contained. 2. There is a large supply of riders, which are carefully graded

and arranged in groups, generally at the ends of the chapters.

Hints are supplied in some cases. 3. The treatment is Euclidean throughout, with a modern

sequence. Practically no numerical work is introduced, that

being left to Practical Geometry. 4. Separate proofs are given of a few corollaries where their

importance seems to demand it. 5. At the end of the book there is a chapter introducing the

pupil to more advanced Geometry, including some riders on

Solid Geometry.

6. There is a set of revision papers.

7. There is a set of hard Miscellaneous Exercises. We have to acknowledge the courtesy of H.M. Stationery Office, of the Oxford and Cambridge Joint Board, of the Oxford Local Examinations Delegacy, of the Cambridge Local Examinations Syndicate, of the Universities of London and Bristol, and of the Board for the Common Examination for Entrance to Public Schools for permission to include exercises from public examination papers.

Finally we have to thank many colleagues and friends for suggestions and criticisms.

A. W. S.

R. T. H. HARROW,

May, 1926.